and we have used the completness relation of coherent state \(\int d^{2}zd^{2}\tilde{z}\left|z\tilde{z}\right\rangle \left\langle z\tilde{z}\right|/\pi ^{2}=1,\)  here \(\left|z\right\rangle \)  and \(\left|\tilde{z}\right\rangle \)  is the coherent state in real and fictitious modes,
respectively, and the formula [1]}
\(& \int \frac{d^{2}z}{\pi }\exp \left( \zeta \left|z\right|^{2}+\xi z+\eta z^{\ast }+fz^{2}+gz^{\ast 2}\right) \\& =\frac{1}{\sqrt{\zeta ^{2}-4fg}}\exp \left[ \frac{-\zeta \xi \eta +\xi ^{2}g+\eta ^{2}f}{\zeta ^{2}-4fg}\right] , \) 
